## Loeb Measures in Practice: Recent Advances: EMS Lectures 1997This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

I | 1 |

II | 2 |

III | 7 |

IV | 10 |

V | 11 |

VI | 13 |

VII | 16 |

VIII | 17 |

XXXVI | 50 |

XXXVII | 52 |

XXXIX | 53 |

XL | 55 |

XLI | 61 |

XLII | 63 |

XLIII | 64 |

XLIV | 66 |

### Other editions - View all

Loeb Measures in Practice: Recent Advances: EMS Lectures 1997 Nigel J. Cutland No preview available - 2000 |

### Common terms and phrases

additional analysis applications approach approximation attractor basic bounded Brownian motion calculus called claim condition consider construction continuous convergence corresponding CRR model defined Definition denote density derivation described developed dimension discrete discussed distributed Editor elements equivalent example existence extension fact finite fixed formula function function F given gives holds hyperfinite idea increments infinitesimal initial integral internal intuitive Lecture Loeb measure Loeb space Malliavin mapping mathematical means methods N.J. Cutland nonstandard Note obtained operator option particular paths precise probability Problems proof properties random representation respect result S-continuous sense sequence simply SL2 lifting solution solve sphere standard statistical solutions stochastic differential equations stochastic Navier-Stokes equations strategy sufficient Suppose Systems term Theorem theory topology Transfer Principle unique VIII Wiener measure write